Optimal. Leaf size=37 \[ -\frac{(x+1)^{12}}{14 x^{14}}+\frac{(x+1)^{12}}{91 x^{13}}-\frac{(x+1)^{12}}{1092 x^{12}} \]
[Out]
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Rubi [A] time = 0.0236464, antiderivative size = 37, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.176 \[ -\frac{(x+1)^{12}}{14 x^{14}}+\frac{(x+1)^{12}}{91 x^{13}}-\frac{(x+1)^{12}}{1092 x^{12}} \]
Antiderivative was successfully verified.
[In] Int[((1 + x)*(1 + 2*x + x^2)^5)/x^15,x]
[Out]
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Rubi in Sympy [A] time = 6.54921, size = 29, normalized size = 0.78 \[ - \frac{\left (x + 1\right )^{12}}{1092 x^{12}} + \frac{\left (x + 1\right )^{12}}{91 x^{13}} - \frac{\left (x + 1\right )^{12}}{14 x^{14}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1+x)*(x**2+2*x+1)**5/x**15,x)
[Out]
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Mathematica [B] time = 0.00403979, size = 79, normalized size = 2.14 \[ -\frac{1}{14 x^{14}}-\frac{11}{13 x^{13}}-\frac{55}{12 x^{12}}-\frac{15}{x^{11}}-\frac{33}{x^{10}}-\frac{154}{3 x^9}-\frac{231}{4 x^8}-\frac{330}{7 x^7}-\frac{55}{2 x^6}-\frac{11}{x^5}-\frac{11}{4 x^4}-\frac{1}{3 x^3} \]
Antiderivative was successfully verified.
[In] Integrate[((1 + x)*(1 + 2*x + x^2)^5)/x^15,x]
[Out]
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Maple [A] time = 0.009, size = 62, normalized size = 1.7 \[ -{\frac{55}{12\,{x}^{12}}}-{\frac{11}{13\,{x}^{13}}}-{\frac{55}{2\,{x}^{6}}}-{\frac{11}{4\,{x}^{4}}}-33\,{x}^{-10}-{\frac{231}{4\,{x}^{8}}}-15\,{x}^{-11}-{\frac{1}{14\,{x}^{14}}}-{\frac{154}{3\,{x}^{9}}}-{\frac{1}{3\,{x}^{3}}}-11\,{x}^{-5}-{\frac{330}{7\,{x}^{7}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1+x)*(x^2+2*x+1)^5/x^15,x)
[Out]
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Maxima [A] time = 0.691704, size = 81, normalized size = 2.19 \[ -\frac{364 \, x^{11} + 3003 \, x^{10} + 12012 \, x^{9} + 30030 \, x^{8} + 51480 \, x^{7} + 63063 \, x^{6} + 56056 \, x^{5} + 36036 \, x^{4} + 16380 \, x^{3} + 5005 \, x^{2} + 924 \, x + 78}{1092 \, x^{14}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 2*x + 1)^5*(x + 1)/x^15,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.263914, size = 81, normalized size = 2.19 \[ -\frac{364 \, x^{11} + 3003 \, x^{10} + 12012 \, x^{9} + 30030 \, x^{8} + 51480 \, x^{7} + 63063 \, x^{6} + 56056 \, x^{5} + 36036 \, x^{4} + 16380 \, x^{3} + 5005 \, x^{2} + 924 \, x + 78}{1092 \, x^{14}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 2*x + 1)^5*(x + 1)/x^15,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.583568, size = 61, normalized size = 1.65 \[ - \frac{364 x^{11} + 3003 x^{10} + 12012 x^{9} + 30030 x^{8} + 51480 x^{7} + 63063 x^{6} + 56056 x^{5} + 36036 x^{4} + 16380 x^{3} + 5005 x^{2} + 924 x + 78}{1092 x^{14}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1+x)*(x**2+2*x+1)**5/x**15,x)
[Out]
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GIAC/XCAS [A] time = 0.268897, size = 81, normalized size = 2.19 \[ -\frac{364 \, x^{11} + 3003 \, x^{10} + 12012 \, x^{9} + 30030 \, x^{8} + 51480 \, x^{7} + 63063 \, x^{6} + 56056 \, x^{5} + 36036 \, x^{4} + 16380 \, x^{3} + 5005 \, x^{2} + 924 \, x + 78}{1092 \, x^{14}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 2*x + 1)^5*(x + 1)/x^15,x, algorithm="giac")
[Out]